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Answers

If there was only one student in the room there would be no one to shake hands with.

If there were only two students in the room, there would be one handshake.

If there were three students, let's call them Ann, Bee and Cindy then:

Ann would shake hands with Bee
Ann would shake hands with Cindy
Bee would shake hands with Cindy

...so there would be three handshakes.

Here's a table showing these results:

No. of Students		No. of Handshakes
.	.	.
1		0
2		1
3		3
4		6
5		10
6		15
7		21
8		28
9		36
10		45
11		55
12		66
13		78
14		91
15		105
16		120
17		136
18		153
19		171
20		190
21		210
22		231
23		253
24		276
25		300
26		325
27		351
28		378
29		406
30		435
31		465
32		496

Can you find a formula?

If instead of handshakes, each student in the room gave every other student a present, how many presents would be given?

Handshakes

A Maths Starter of The Day

Answers